(875.) In this manner Coulomb determined the distribu- for which may in each case be expanded into a series, 
Result. joaor electricity upon electrified spheres at and after the co-efficients of the terms of which (known as 
contact with one another;—on spheres inductively Laplace’s co-eflicients) are connected by certain rela- 
electrified,—on rods and plates and other figures; and tions which are evolved from the conditions of the 
his results, so far as they have been compared with problem. It was M. Biot first of all, but principally 
theory, give evidence of the care and skill with which Poisson, who applied this method to electrical, and 
they were obtained, allowance being in all cases made subsequently to magnetical phenomena. Poisson, 
for the loss of electricity by imperfect insulation. He with great labour, succeeded in representing correctly 
also laboured with praiseworthy diligence to compare by analysis the conditions of some of Coulomb's ex- 
his results with the theory which he adopted of two periments on spheres and ellipsoids. But it must 
fluids, each attracting the particles of the other and be owned that the complication of the analysis, the 
repelling their own according to the Newtonian law. difficulty of applying it to any but the very simplest 
The Hpinian theory admits of only one fluid, but as it cases, and the considerable latitude of the errors of 
assumes a repulsion between the elementary particles experiment, rendered the results rather analytical 
matter it cannot be said to gain much in simplicity, exercises than solid bases for physical induction ; 
whilst the mathematical results of either hypothesis which may in some degree account for the manner 
are in general the same. M. Mosotti has endea- in which Sir John Leslie mentions them in his Dis- 
. voured recently to revive the view of Franklin and sertation. Poisson (as I have elsewhere remarked) 
of ZZpinus, so as to include, after the manner of had not the talent of conducting his mathematics in 
Boscovich, the entire mechanical properties of a fertile direction, and usually left the fields of ex- 
matter. perimental physics on which he touched nearly as 
(876.) The doctrine of attractions is a complex and diffi- barren as he found them. But this is no rea- 
cunt h as cult one even when the distribution of the attracting son why other mathematical reasoners may not 
‘ attractions Matter, as well as the fundamental law of attraction, obtain more pregnant results. We shall see in the 
i and repul- is known. But it becomes much more so when the next section that Gauss, a distinguished contempo- 
)_ sions. distribution of the attracting matter is itself the rary of Poisson, by treating the great problem 
1 result of the very effect which it is the object of the distribution of the magnetism of the globe 
| of the problem to discover. If two homogeneous (in many respects similar to those of the theory 
! spheres attract one another, molecule to molecule, by of electricity) with the utmost mathematical gene- 
the law of gravity, the problem is easy, provided the rality, has obtained results of great novelty and 
matter be rigid, and the distribution of it therefore importance ; that he has not only shown experi- 
unchanged ; but if two such spheres be charged with menters how to proceed, but has invented instru- 
the mobile electric fluid (using the term as a mere ments for them to use, A similar step has not yet 
abbreviation), the case is very different, for now the been taken in electricity. Notwithstanding the un- 
electricity tends to shun the nearest points of each questionable beauty of Sir William Harris’s methods 
sphere, and to accumulate itself towards the remoter of measuring electrical attractions (Phil. T'rans, 
parts of their surfaces. The distribution of the 1834), they are little adapted for comparison with 
electricity, and also the repulsive effect at any point, theory, and Coulomb’s experiments still remain the 
are both to be found simultaneously, The caleula- standard ones on the subject. 
tions of Coulomb were inadequate (as has been said) The theory of Coulomb has, however, been ably ge- (878.) 
to such a solution ; he contented himself with comput- neralized by Green, a nearly self-taught mathemati- Writings 
ing the effect of certain simple distributions which evi- cian of great originality, who died at a premature age. ° 4 - 
dently lay on opposite sides of the truth, and com- In a memoir on electricity privately printed about professor 
paring them with the result of experiment. Though 1830 he generalized Poisson’s methods and ap- W-Thom- 
any one such comparison might avail little, the plied them to a number of new cases. His paper *°™ 
cumulative evidence of many imperfect comparisons was reprinted a few years since in Crelle’s Journal. 
argued favourably for the truth of the hypothesis. To him I believe is due the term potential. Several 
(877.) At the very time that Coulomb was pursuing this continental mathematicians of eminence have added 
Its prin- inquiry, Legendre first, and then Laplace, were in- some steps to the theory of electricity, but probably 
ciples de- venting and improving those subtle and powerful the most important from its fertility and simplicity 
veloped by 
Coulomb, 
7 
Cuar. VII., § 7.] 
ing handle, which being applied flat-wise to the sur- 
face of an excited body takes off a portion of electri- 
city, which is found in all cases to be proportioned 
to the electric excitement of the part which it had 
touched; being then presented to the torsion balance 
properly electrified, it shows by the repulsive effect 
produced, the relative tension of the part of the 
body whence the sample was obtained. 
mathematical methods at which we have glanced in 
ELECTRICITY.—COULOMB—POISSON—GREEN. 
989 
the chapter on Physical Astronomy, Art. 99, &c., Laplace, 
for estimating attractions by a general method. Le- ae Pois- 
f ne 
gendre’s principles of calculation applied to cases o 
the symmetrical distribution of the attractive sub- 
stances, but Laplace escaped this restriction. The 
problem is reduced to finding a quantity usually de- 
noted by the letter V, called by some writers the 
potential, for the given body or surface, the expression Potential. 
is a theorem discovered by Professor William Thom- 
